[Paper Review] Exotic Implications of Electron and Photon Final States

Lisa Randall, Mark B. Wise|ArXiv.org|Jul 10, 2008

Quantum Mechanics and Applications3 citations

TL;DR

The paper demonstrates that a TeV-scale resonance decaying to both $e^+e^-$ and $\gamma\gamma$ final states with comparable branching ratios implies direct coupling of electrons to new physics, ruling out spin-1 or spin-0 models without direct electron interactions. The Randall-Sundrum Kaluza-Klein graviton is uniquely predicted to exhibit a $\text{Br}(\gamma\gamma)/\text{Br}(e^+e^-) = 2$ ratio, enabling identification without spin measurement.

ABSTRACT

New resonances with masses of order a few ${ m TeV}$ might be discovered at the LHC. We show that no resonance that couples to electrons only through Standard Model interactions can decay to both $e^+e^-$and $γγ$ with significant branching ratios. This means that finding both electron-positron and two-photon final states is evidence that electrons couple directly to the new physics associated with the resonance and furthermore that the resonance is not spin-1. The least fine-tuned such examples involve electron compositeness. One such example, Kaluza Klein excitations of the graviton in the version of the Randall Sundrum Model where Standard Model matter is located on the ${ m TeV}$ brane, can be distinguished from other possibilities by its predicted branching fractions into the two modes.

Motivation & Objective

• To determine whether observing both $e^+e^-$ and $\gamma\gamma$ final states in a TeV resonance signals direct electron coupling to new physics.
• To identify theoretical models that can naturally support comparable branching ratios to $e^+e^-$ and $\gamma\gamma$.
• To establish a selection rule distinguishing resonances that couple directly to electrons from those that decay via SM interactions only.
• To demonstrate that the Randall-Sundrum KK graviton is uniquely identifiable by its predicted branching ratio ratio $\text{Br}(\gamma\gamma)/\text{Br}(e^+e^-) = 2$.
• To provide a robust, model-independent method for probing new physics at the LHC using relative branching fractions.

Proposed method

• Analyzing tree-level decay amplitudes for spin-0, spin-1, and spin-2 resonances to $e^+e^-$ and $\gamma\gamma$ final states.
• Applying helicity suppression arguments showing that $e^+e^-$ decay amplitude for spin-0 resonances is proportional to $m_e$, vanishing in the massless limit.
• Using effective field theory to model the coupling of the KK graviton to the SM stress tensor via $\mathcal{L}_{\text{int}} = \kappa h^{\text{KK}}_{\mu\nu} T^{\mu\nu}_{\text{SM}}$.
• Calculating decay rates using $\Gamma = \kappa^2 f M^3 / (80\pi)$, with $f$ factors from Table 1 for different final states.
• Comparing branching ratios across final states to derive the prediction $\text{Br}(\gamma\gamma)/\text{Br}(e^+e^-) = 2$ for the RS KK graviton.
• Applying constraints from flavor-changing processes to rule out direct electron coupling in most models unless protected by gauge symmetry or compositeness.

Experimental results

Research questions

• RQ1 Can a resonance decay to both $e^+e^-$ and $\gamma\gamma$ with significant branching ratios if electrons only couple to it via SM interactions?
• RQ2 What selection rules govern the simultaneous observation of $e^+e^-$ and $\gamma\gamma$ final states in TeV-scale resonances?
• RQ3 Why is the Randall-Sundrum KK graviton uniquely identifiable by its branching ratio ratio $\text{Br}(\gamma\gamma)/\text{Br}(e^+e^-) = 2$?
• RQ4 How does electron compositeness or direct coupling to new physics affect the branching ratios to $e^+e^-$ and $\gamma\gamma$?
• RQ5 Can relative branching fractions serve as a viable alternative to angular distributions for spin measurement at the LHC?

Key findings

• A spin-0 resonance cannot decay to $e^+e^-$ at tree level with significant branching ratio if the electron mass is neglected, due to helicity suppression.
• Resonances that decay to both $e^+e^-$ and $\gamma\gamma$ with comparable branching ratios must involve direct coupling of electrons to the new physics, excluding SM-mediated decays.
• The only known scenario with a natural, non-fine-tuned explanation for comparable branching ratios is the Randall-Sundrum KK graviton with brane-localized SM fields.
• The RS KK graviton predicts a precise branching ratio ratio $\text{Br}(\gamma\gamma)/\text{Br}(e^+e^-) = 2$, derived from $f$ factors in Table 1.
• This ratio allows identification of the RS KK graviton even without spin measurements, providing a powerful experimental signature.
• The branching fractions are predicted to be $\text{Br}(h^{\text{KK}} \to e^+e^-) \simeq 0.022$ and $\text{Br}(h^{\text{KK}} \to \gamma\gamma) \simeq 0.044$ when only SM final states are considered.